# I Description of Adiabatic Expansion

1. Nov 10, 2018

### I_laff

I've seen the derivation for the adiabatic expansion of an ideal gas which gives the result $TV^{\gamma - 1} = constant$ which I understand. I have also seen the a similar result, $pV^{\gamma} = constant$. But I can't see how to get from the first expression to the second. Any ideas?

2. Nov 10, 2018

### hilbert2

If you put $\frac{PV}{nR}$ in place of $T$ in the first equation, doesn't it become the second one, assuming that the number of moles $n$ remains constant in the expansion?

3. Nov 10, 2018

### I_laff

From doing that you get $pV^{\gamma} = R(constant)$. So you just define a new constant on the RHS that contains $R$?

4. Nov 10, 2018

### sophiecentaur

Isn't this a straightforward bit of Text Book derivation? Do you not have access to one?

5. Nov 10, 2018

### hilbert2

Yes, it's a different constant then, the original one multiplied by $nR$.

6. Nov 10, 2018

### sophiecentaur

If you don't have a text book, try the Hyperphysics website. They have a fair amount of stuff on the gas laws.

7. Nov 10, 2018

### I_laff

You are probably right, however I don't have a textbook on thermodynamics. I thought of substituting $\frac{pV}{nR}$ but didn't see how to remove $nR$ from the final expression. Since they're constant, I guess it's obvious the new constant contains these terms.

8. Nov 10, 2018

### I_laff

Thanks, I'll check it out .

9. Nov 10, 2018

### sophiecentaur

There are other on-line sources which are an alternative to a text book but Hyperphysics is fairly user friendly.